Welcome to the UTK Mathematical Life Sciences Page for Education
This collection of Pages has been organized by Susan Harrell and Monica Beals under the supervision of Louis Gross at the University of Tennessee, Knoxville, with support from the National Science Foundation Undergraduate Course and Curriculum Program through Award DUE-9752339, "Alternative Routes to Quantitative Literacy for the Life Sciences".
General Biology Modules
****** These pages are drafts and should not be modified or reproduced in any way ******
Cell Structure and Growth
Cell Division and Rates of Population Growth -- exponential and geometric equations, sequences
Cell Division and the Presence of a Growth Factor -- exponential and hyperbolic equations
Doubling Time of Tumors -- ratios, linear regression
Maintenance of Cell Shape -- simple algebra, reading a chart
Mechanisms of Cell Attachment -- simple equations, geometry, interpreting graphs
Mitotic Index and Cell Division -- ratios, reading a chart
Nuclear and Cytoplasmic Viscosity -- linear equations
Nucleo-cytoplasmic Transport -- exponential equations
Nucleoplasmic Index -- ratios, interpreting graphs
Permeability of Molecules through the Cell Membrane -- linear regression, log-log plots
Cell Aggregation and Sphere Packing -- geometry, ratios, inequalities
Cellular Processes
Antibody Binding -- hyperbolic and linear equations
Chemoreception -- hyperbolic and linear equations
Diffusion Through a Cell Membrane -- calculus, rates of change, linear and hyperbolic equations
Enzymes and the Rate of Chemical Reactions -- calculus, rates of change, hyperbolic equations
Gibb's Free Energy -- ratios, logarithms, exponents
Efficiency of ATP Production -- ratios
Maintaining Cellular Conditions: pH and Buffers -- logarithms, exponents, ratios
Metabolism for Energy and the Respiratory Quotient -- quotients, ratios
Water Movement through a Membrane: The Van't Hoff Equation --inequalities, simple algebra
Genetic Information
Amino Acid Frequency -- probability, linear regression
DNA and Knot Theory -- topology
Half Life of mRNA -- exponential and logarithmic equations
Genetics and Evolution
Body Size Constraints in Xylem Feeding Insects: Allometric Relationships -- exponential equations, ratios, logarithmic scales
The Chi-Square Test -- probability, statistical testing
Hardy-Weinberg Equilibrium -- frequencies
Population Bottlenecks: Heterozygosity vs. Allelic Diversity-- basic algebra, ratios, exponential functions
Population Genetics: Limits to Adaptation-- basic algebra, logarithms
Ecology
Cohort Life Tables -- functions
Diversity Indices: Simpson's D -- functions
Diversity Indices: Shannon's H -- functions
Estimating Tree Heights: Right Triangle Trigonometry -- trigonometric functions
Interspecific Competition: the Lotka-Volterra Model -- differential equations, state-space graphs
Optimal Foraging Theory -- inequalities
Predator-Prey Dynamics: the Lotka-Volterra Model -- differential equations
Species-Area Relationships -- exponential and logarithmic equations
Type I Functional Response -- linear functions
Type II Functional Response -- Holling's Disk Equation
Biomechanics, Structure, and Function
Sizes of Organisms: The Surface Area to Volume Ratio -- geometry, ratios
Stress-Strain Curves and Young's Modulus -- ratios
Plant Physiology
Energy Absorbed From Light During Photosynthesis -- ratios, hyperbolic equationsCoordinating Photosynthetic Activity: Circadian Rhythms -- trigonometry, sine waves
Nastic Movements in Plants --hyperbolic equations, interpreting models
Plant Cell Expansion and Plant Hormones -- hyperbolic equations
Phototropism and Gravitropism: Quantifying Stem Curvature -- geometry, trigonometry
Quantitative Cytological Characteristics: Photorespiration - ratios, reading a chart
Translocation of Nutrients in the Phloem: Dixon's Paradox -- linear equations, linear regression
Translocation of Nutrients in the Phloem: Poiseuille's Equation -- hyperbolic equations, calculus, rates of change
Animal Physiology
Cardiac Output -- proportions, linear equations, linear regression
Hemoglobin Evolution -- parabolic and hyperbolic equations, calculus, finding maxima
Lung Capacity and Rhythms in Breathing -- trigonometry, sine waves
Muscle Contraction -- hyperbolic functions, plotting data
Osmoregulation -- logarithmic equations
Oxygen Diffusion in Simple Organisms -- parabolic and linear equations
Sperm Motility -- square roots, parabolic equations
Synapse Transmission and Action Potentials -- inequalities,
Tension in Blood Vessels: LaPlace's Equation -- linear equations
You can also check out our General Biology Reform links
and the working version of our Glossary of Biology Terms
Copyright 1999 M. Beals, L. Gross, S. Harrell